English term (edited): trotted bedpans

The line you give us is from a short story, 'All you Zombies-" written in 1959 by Robert A. Heinlein. The film 'Predestination' is based on the story, and lifts some of the narrative from it. It was set in (what was then the future) New York City 1970. The person speaking here tells of being kicked out by the family where she was a mother's helper when she discovered that she was pregnant, and the orphanage where she grew up wouldn't take her back either. From what I can see, her pregnancy wasn't full term at that point, but she ended up in the charity ward of the hospital and I reckon she was there to help out until she was full term as a way of having somewhere to live until she gave birth.

In George Orwell's 'How The Poor Die', he describes his experiences in a non-paying, charity patient in a Parisian hospital in 1929. In it, he tells of some of the patients carrying out work which we would expect nurses to do - "It was generally patients, too, who carried the bed-bottles and the grim bed-pan". Some of the 'malingerers' helped out with some of the nurses duties so that they could justify staying for longer than they needed too. So, I thought it might be that in this story, she ran back and forth with the bedpans of her fellow patients who were unable to do so themselves (as a way of earning her keep until she was full term).

In 'Stranger In A Strange Land' by Robert Heinlein, the character who was once a nurse says of herself,
"I am not sure where I will be, or whether I will remember that I was once Jill Boardman who was happy trotting bedpans and equally happy strutting her stuff ...". So, I think this backs up my theory that it means that she's running back and forth with bedpans.
https://archive.org/stream/StrangerInAStrangeLandRobertAHein...

According to Merriam Webster dictionary, trotting is the "jogging gait of a human that falls between a walk and a run", and on the trot means "busy all the time".

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Note added at 2 days 19 hrs (2021-06-15 13:44:19 GMT)
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'Quiet Warriors' by Blake E. Edwards also contains the term "trotting bedpans" in the sense of running to and fro to empty and return patients bedpans -
"As most of my patients are ambulant, I am relieved of trotting bedpans, water, food etc., but the "chow cart," emptying the garbage, paper waste and two hours of drill and class keep me busy most of the day, besides keeping the ward clean"
https://books.google.co.uk/books?id=neSNAAAAQBAJ&pg=PA90&lpg... (page 90)

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Note added at 2 days 21 hrs (2021-06-15 15:34:12 GMT)
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Further examples of trotting water in a book and academic studies.

In 'A Land to Call Home' by Lauraine Snelling -
"They assigned Penny to trot water to the workers and two of the younger girls to oversee the small children"
https://www.google.co.uk/books/edition/A_Land_to_Call_Home/m...

Complementing Water Supply through Rainwater Harvesting in Some Selected Villages of Sahel Savannah Ecological Zone in Borno State Northeastern Nigeria - Ishaku, Abayomi, Sahabo, Dama
"Adequate safe water supply implies that the time spent by women and children in trotting water can be used for other productive works that will improve the living standard of the households...On the distances covered to nearest water sources, it was reported that about 60% of household walk distances more than 2 km to trot water and 16% walk less than 1 km while 25% walk for 2 km to get water especially during the dry seasons. "
https://www.researchgate.net/publication/276045313_Complemen...

Water Supply Dilemma in Nigerian Rural Communities: Looking towards the Sky for an Answer -Ishaku, Majid, Ajayi, Haruna
"This situation forces households especially the women and children to spend more time walking longer distances during the dry season to trot water for domestic purposes."



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Note added at 2 days 21 hrs (2021-06-15 15:34:39 GMT)
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Forgot the link
https://file.scirp.org/Html/4-9401351_6993.htm